Problem: Simplify the following expression: $x = \dfrac{6n^2 + 48n - 54}{n - 1} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ x =\dfrac{6(n^2 + 8n - 9)}{n - 1} $ Then we factor the remaining polynomial: $n^2 + {8}n {-9} $ ${-1} + {9} = {8}$ ${-1} \times {9} = {-9}$ $ (n {-1}) (n + {9}) $ This gives us a factored expression: $\dfrac{6(n {-1}) (n + {9})}{n - 1}$ We can divide the numerator and denominator by $(n + 1)$ on condition that $n \neq 1$ Therefore $x = 6(n + 9); n \neq 1$